RC22846 (W0307-128) July 15, 2003 Physics IBM Research Report Remote Coulomb Scattering in Metal-Oxide-Semiconductor Field-Effect Transisitors: Screening by Electrons in the Gate Francisco Gamiz 1 , Massimo V. Fischetti IBM Research Division Thomas J. Watson Research Center P.O. Box 218 Yorktown Heights, NY 10598 1 University of Granada Spain Research Division Almaden - Austin - Beijing - Delhi - Haifa - India - T. J. Watson - Tokyo - Zurich LIMITED DISTRIBUTION NOTICE: This report has been submitted for publication outside of IBM and will probably be copyrighted if accepted for publication. It has been issued as a Research Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution outside of IBM prior to publication should be limited to peer communications and specific requests. After outside publication, requests should be filled only by reprints or legally obtained copies of the article (e.g. , payment of royalties). Copies may be requested from IBM T. J. Watson Research Center , P. O. Box 218, Yorktown Heights, NY 10598 USA (email: [email protected]). Some reports are available on the internet at http://domino.watson.ibm.com/library/CyberDig.nsf/home .
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RC22846 (W0307-128) July 15, 2003Physics
IBM Research Report
Remote Coulomb Scattering in Metal-Oxide-SemiconductorField-Effect Transisitors: Screening by Electrons in the Gate
Francisco Gamiz1, Massimo V. Fischetti
IBM Research DivisionThomas J. Watson Research Center
P.O. Box 218Yorktown Heights, NY 10598
1University of GranadaSpain
Research DivisionAlmaden - Austin - Beijing - Delhi - Haifa - India - T. J. Watson - Tokyo - Zurich
LIMITED DISTRIBUTION NOTICE: This report has been submitted for publication outside of IBM and will probably be copyrighted if accepted for publication. It has been issued as a ResearchReport for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution outside of IBM prior to publication should be limited to peer communications and specificrequests. After outside publication, requests should be filled only by reprints or legally obtained copies of the article (e.g. , payment of royalties). Copies may be requested from IBM T. J. Watson ResearchCenter , P. O. Box 218, Yorktown Heights, NY 10598 USA (email: [email protected]). Some reports are available on the internet at http://domino.watson.ibm.com/library/CyberDig.nsf/home .
Note that in the case ox = poly, and setting the origin at the oxide-silicon interface, the
Green’s functions (Equations 3-5) are reduced to Expression 11 of Ref.[11], corresponding
to the previous scattering model with very thick oxide layers (tox → ∞). It is easy to addthe effect of screening by free carriers in the gate following this scheme. To add the effect of
screening by free carriers in the gate we need only replace in expressions 6,7 and 8 poly by
poly
¡√2Q,ω → 0
¢, following Appendix B in Ref.[12].We have considered a Thomas-Fermi
type dielectric function for poly
¡√2Q,ω → 0
¢[14]:
poly
³√2Q, z
´= poly
Ã1 +
e2npoly
polykBT¡√2Q¢2!
(9)
kB being the Boltzmann constant, e the electron charge, T the temperature and npoly
the average density of free electrons in the "depleted" region of the poly gate. Note that
according to Expressions 3 to 8 electrons in the gate not only screen the charged centers due
to the poly depletion, but also screen the impurities in the silicon substrate.
Figure 2 shows that the distribution of free electrons in the gate, n3D (z), is not uniform
across the polysilicon depletion region. Since the treatment of the dielectric response of an
inhomogeneous electron gas is a formidable problem still largely unsolved, different choices
could be made to evaluate npoly:
i) npoly could be set equal to the electron concentration at the poly/oxide interface, i.e.,
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npoly = n3D (z = 0) ; (10)
as shown below, using the surface concentration will severely underestimate the mobility
(as it will underestimate screening for most of the impurities).
ii) A second choice for npoly could be the average of n3D (z) over the depletion region:
npoly =
R 0−Wdepl
n3D (z) dz
Wdepl(11)
Wdepl being the thickness of the polygate depletion region. This latter choice will overesti-
mate the mobility (as it will overestimate screening of the impurities closer to the channel).
These two approaches will "bracket" the actual effect of the screening. This is why we
propose the following:
iii) A third choice for npoly has been considered, in which the electron distribution is
weighted with the net charge in the gate, Qgate(z) :
npoly =
R 0−L1 n3D (z)Qgate (z) dzR 0
−L1 Qgate (z) dz(12)
Using a Monte Carlo simulator (detailed elsewhere) we have evaluated electron mobil-
ity taking into account the effect of RCS and the screening by the electrons in the gate.
The different choices of npoly have been considered. Phonon scattering, surface roughness
scattering (Lsr = 1.3nm,and ∆sr = 0.3nm), and Coulomb scattering due to the impurities
in the substrate have been considered (NA = 5x1017cm−3). Figure 3 shows mobility curves
versus the transverse effective field for two values of the silicon thickness, Tox = 1nm, (upper
graph)a and Tox = 5nm (lower graph). Dashed lines correspond to mobility curves when
RCS is ignored, and solid squares correspond to mobility curves when screening by gate
electrons is ignored. Curves with open symbols correspond to mobility curves taking into
account RCS, and the different choices of screening by electrons in the gate. An immediate
observation is that for Tox = 5nm, the effect of RCS is negligible (as reported in Ref.[7]), and
therefore screening hardly modifies the mobility curves. However, for Tox = 1nm, the RCS
effect is important, and therefore screening by electrons in the gate becomes noticeable. As
mentioned above, when the first option is considered for npoly (open triangles), the screening
is underestimated and the electron mobility curve almost coincides with the mobility curve
when screening is ignored. In contrast, when the second option is selected (open circles)
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the screening is overestimated, the scattering is strongly weakened, and the mobility curve
in this case almost coincides with the mobility curve when the RCS effect is ignored. It
can be seen that the mobility curve strongly depends on the choice of npoly to evaluate the
screening by electrons in the gate. It is expected that mobility curves obtained using the
third choice would be nearer the actual result, since the electron distribution is weighted
by the net charge in the depleted region, which is ultimately responsible for RCS. Finally,
Figure 4 shows mobility curves taking into account the effect of RCS and the screening of
the electrons in the gate using the third choice for npoly, for different values of the oxide
thickness. As can be seen, the separation between the mobility curves is now much less
than when the screening by electrons in the gate is ignored. This curve gives us an idea
of the actual dependence of the mobility on the oxide thickness. In summary, the effect of
screening of RCS by free electrons in the polysilicon gate of a MOSFET has been analyzed.
We have included the effect of screening by electrons in the gate on Remote Coulomb scat-
tering due to the charges in the polysilicon depletion layer. Using a Monte Carlo simulator
we have studied the effect of the screening by electrons in the gate, and we have seen that
although the RCS effect is certainly weakened, it is still important for very thin oxide layers
(Tox < 2nm), and therefore should be taken into account.
This work has been carried out within the framework of Research Project No. TIC-2001-
3243 supported by the Spanish Government.
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References
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2 A.Chin, W.J.Chen, T.Chang, R.H.Kao, B.C.Lin, C.Tsai, and J.C.M-Huang, IEEE Electron
Device Lett. 18, 417 (1997)
3 M. S. Krishnan, Y. C. Yeo, Q. Lu, T.J. King, J.Bokor, and C. Hu, Tech.Dig. Int. Electron
Devices Meeting IEDM-98, pp.571-574 (1998)
4 M.S.Krishnan, L.Chang, T.King, J.Bokor, and C.Hu, Tech.Dig. Int. Electron Devices Meeting